All electric piezoelectric finger sensor (pefs) for soft material stiffness measurement

ABSTRACT

A PEFS (Piezoelectric Finger Sensor) acts as an “electronic finger” capable of accurately and non-destructively measuring both the Young&#39;s compression modulus and shear modulus of tissues with gentle touches to the surface. The PEFS measures both the Young&#39;s compression modulus and shear modulus variations in tissue generating a less than one-millimeter spatial resolution up to a depth of several centimeters. This offers great potential for in-vivo early detection of diseases. A portable hand-held device is also disclosed. The PEF offers superior sensitivity.

This application is a continuation of U.S. patent application Ser. No.14/017,508, currently pending, which in turn is a continuation of U.S.patent application Ser. No. 13/268,225, filed on Oct. 7, 2011, now U.S.Pat. No. 8,459,933 issued on Oct. 8, 2013 which in turn, is acontinuation of, U.S. patent application Ser. No. 12/837,590, filed onJul. 16, 2010, now U.S. Pat. No. 8,033,185 issued on Oct. 11, 2011;which, in turn, is a continuation of U.S. patent application Ser. No.12/328,639, filed on Dec. 4, 2008, now U.S. Pat. No. 7,779,707 issued onAug. 24, 2010, which, in turn, is a continuation of U.S. patentapplication Ser. No. 11/136,173, filed on May 24, 2005, now U.S. Pat.No. 7,497,133, issued on Mar. 3, 2009 which in turn, is anon-provisional of U.S. Provisional Application No. 60/573,869, filedMay 24, 2004, the entire disclosures of which are hereby incorporated byreference as if set forth fully herein.

STATEMENT OF GOVERNMENT INTEREST

This invention was reduced to practice with Government support underGrant No. RO1 EB00720-01 awarded by NIH; the Government is thereforeentitled to certain rights to this invention.

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention relates to a piezoelectric sensor for measuringshear and compression. 2. Brief Description of the Prior Art

A typical soft-material/tissue mechanical property tester requires anexternal force (displacement) applicator and an external displacement(force) gauge.^(1,2) The external force (displacement) generator may behydraulic or piezoelectric and the external displacement gauge (forcegauge) may be optical or piezoelectric. Regardless of the mechanism offorce/displacement generation and displacement/force detection, typicaltissue/soft-material mechanical testing is destructive and it requiresspecimens cut to a disc shape to fit in the tester. In addition, acompressive elastic modulus tester e.g., an Instron is also differentfrom a shear modulus tester, e.g., a rheometer.³ Currently, no singleinstrument measures both the compressive Young's modulus and the shearmodulus.

Over the past decades, many techniques have been developed to imagetissue structures.⁴⁻⁹ Computer Tomography (CT)¹⁰ takes 360 degree X-raypictures and reconstructs 3D tissue structures using computer software.Magnetic Resonance Imaging (MRI)¹¹ uses powerful magnetic fields andradio waves to create tissue images for diagnosis. Ultrasound (US)¹²transmits high-frequency waves through tissue and captures the echoes toimage tissue structures. T-scan (TS)¹³ measures low-level bioelectriccurrents to produce real-time images of electrical impedance propertiesof tissues. Ultrasound elastography (UE)¹⁴ evaluates the echo timethrough tissues under a constant mechanical stress and compares it tothat of the same tissue when unstressed. A tissue strain map is thenobtained, from which an image of 2D elastic modulus distribution iscreated by inversion techniques. Tactile imaging tools using arraypressure sensors probe spatial tissue stiffness variations. However noneof these techniques have the ability to probe tumor interfaceproperties.

The detection of abnormal tissue as cancerous growth requiresimprovements in screening technologies. The key to successful treatmentlies in early detection. Imaging techniques such as mammography inbreast cancer screening, detect abnormal tissue by tissue densitycontrast. Mammography is the only FDA approved breast cancer screeningtechnique, which has a typical sensitivity of 85% that decreases to 65%in radiodense breasts.¹⁰ However, in these screening processes there isa high incidence of false positives. In fact, only about 15-30% ofbreast biopsies yield a diagnosis of malignancy. Changes in tissuestiffness have increasingly become an important characteristic indisease diagnosis. It is known that breast cancers are calcified tissuesthat are more than seven times stiffer than normal breast tissues.¹¹⁻¹⁴Thus, contrasting levels of stiffness within the breast may indicatecancerous tissue. Similarly, plaque-lined blood vessels are also stifferthan normal, healthy blood vessels.

The examining physician may detect abnormal tissue stiffness bypalpation by taking advantage of the fact that cancerous tissues arestiffer than surrounding normal tissues under compression. Thus,palpation has been a useful tool for experienced physicians to diagnosebreast and prostate cancer. However, palpation is not quantitative anddepends solely on the experience of the individual physician. So thereremains a critical need to improve cancer-screening technology to reducethe number of unnecessary biopsies.

SUMMARY OF THE INVENTION

In a first aspect, the invention relates to a sensor for measuring acompression modulus and a shear modulus that has a first layer made ofpiezoelectric material, a second layer made of a non-piezoelectricmaterial, a first electrode placed on top of the first layer for sensinga displacement of the first layer; and a second electrode placed on topof the first layer for providing a force to the first layer.

In a second aspect of the invention a sensor for measuring a compressionmodulus and a shear modulus is provided having a first layer made ofpiezoelectric material for providing a force, a second layer made ofnon-piezoelectric material, and a third layer made of piezoelectricmaterial for sensing a displacement.

In a third aspect of the invention a method for measuring a compressionmodulus and a shear modulus is provided. The method has the steps ofproviding a plurality of sensors made of a piezoelectric material and anon-piezoelectric material at a target, applying a force with at leastone of the plurality of sensors, detecting a displacement with at leastone of the plurality of sensors, and providing a measurement of acompression modulus and a shear modulus of said target.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic of two PZT/stainless steel cantilevers with (a)driving and sensing electrodes both on the top side and (b) with abottom sensing PZT layer.

FIG. 2 shows a graph of (a) the displacement signals captured by thesensing PZT layer, and (b) the deflection signal captured by the sensingPZT layer.

FIG. 3 shows a graph of peak and displacement measurements.

FIG. 4 shows a representation and schematic of the compressionindentation tests.

FIG. 5 shows (a) a regular compression test where the contact area isthe same as the surface area, and (b) deformation of a sample in aregular compression test under an applied voltage, V.

FIG. 6 shows a comparison of the elastic modulus obtained in a regularcompression test and an indentation compression test.

FIG. 7 shows (a) a 3-D plot of raw elastic modulus data from indentationtests, (b) the corresponding contour plot, (c) smoothed data, to createan enhanced image, and (d) a representation of the simulated tissue.

FIG. 8 shows graphs of the elastic modulus profile of (a) 7 mm diameterwax in gelatin at various depth measured with a 3 mm wide cantilever,(b) 15 mm diameter wax in gelatin measured with a 5 mm wide cantilever,and (c) summary of the detection depth limit of 3 mm wide cantilever and5 mm wide cantilever.

FIG. 9 shows a schematic of a regular shear test using an L-shapedcantilever where the contact area is the same as the sample surfacearea.

FIG. 10 shows a schematic of an indentation shear test using an L-shapedcantilever where the contact area is much smaller than the samplesurface area.

FIG. 11 shows schematics of (a) regular compression, (b) indentationcompression, (c) regular shear, and (d) indentation shear measurementsusing a cantilever that has a U-shaped stainless steel tip.

FIG. 12 shows a graph of the results of regular compression, indentationcompression, regular shear, and indentation shear measurements on rubbersamples that had a young's modulus 400-500 kPa using the U-shapedcantilever as shown in FIG. 11.

FIG. 13 shows a representation of model tumors and surrounding tissue.

FIG. 14 shows a graphical representation of Young's modulus and shearmodulus tests measured by indentation compression and indentation sheartests on various materials.

FIG. 15 shows a graph of a lateral elastic modulus profile of alumpectomy sample.

FIG. 16 shows (a) a graph of Young's modulus (E) and shear modulus (G)profiles, and (b) G/E profile on breast tissue with cancer.

FIGS. 17A and 17B show a graph of elastic modulus, E, profiles measuredusing an 8 mm wide PEF (open squares) and a 4 mm wide PEF (open squares)on a 15 mm diameter clay inclusion in gelatin.

FIG. 18 shows a representation of a direct tumor mobility measurementmade on a model rough inclusion (front) and on a model smooth inclusion(back) in gelatin using two PEFs.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

A “PEFS” includes a piezoelectric layer bonded to a non-piezoelectriclayer to form a cantilever. FIG. 1 a shows a schematic of a leadzirconate titanate (PZT)/stainless steel cantilever with both thedriving and sensing electrodes on the top side. FIG. 1 b shows aPZT/stainless steel cantilever with a bottom PZT sensing layer. In theseschematics, the PZT represents the piezoelectric layer and the stainlesssteel represents the non-piezoelectric layer.

In a first aspect of the invention, the PEFS is capable ofsimultaneously applying a force and detecting the correspondingdisplacement. The application of a voltage at the driving electrodegenerates the force and the corresponding displacement is measured bydetecting the induced piezoelectric voltage within the sensingelectrode. The PEFS can measure both the compressive Young's modulus andthe shear modulus of a soft material through the cantilevered tip. Thus,in an aspect of the current invention, the PEFS measures both thecompressive Young's modulus and shear modulus using one single device,while at the same time increasing the sensitivity and accuracy of themeasurements, relative to some commercially available devices used forthis purpose. Comparisons between the shear and compressive measurementsusing one single device provide clear and accurate information about theinterfaces between hard inclusions (tumors) and the surrounding tissuethat otherwise could likely not be obtained.

In another aspect of the invention, several PEFS can form an array tomeasure lateral and in-depth stiffness variations in soft-materials andtissues both under compression and under shear. This ability toself-excite via the driving voltage and self-detect via the sensingelectrode allows a PEFS to measure the elastic and shear properties ofspecimens having complex shapes.

In another aspect of the invention, the PEFS may apply forces andmeasure displacements at the same time, allowing the device to functionusing completely electrical means for tissue-stiffness imaging, cancerand disease detection. Thus, the PEFS may be powered with a DC powersource allowing the PEFS to take electrical measurements in the DC mode.In this aspect of the invention the PEFS may be part of a portablehand-held device for measuring tissue. This simple all-electricalmeasurement makes the PEFS look and work like a finger, which may allowfor in vivo measurements in tight spaces.

While the sensitivity of the PEFS has been improved by the increasedsensitivity of the compression tests with the addition of the shear testto the PEFS, the reduction of the probe size as compared to thebulkiness of current tactile cancer-imaging devices, provides increasedversatility as well. In particular, the finger-like shape of the PEFS isnow suitable for, for example, prostate cancer detection.

In another aspect of the invention, the PEFS can analyze measurements ofvarious widths allowing the direct experimental determination of astiffness variation in the thickness direction. Current tumor imagingtechniques are incapable of directly measuring a tumor size or position.Instead, these techniques measure the surface mechanical response. Thetumor information is generated numerically by the “inversion” techniqueand used to reconstruct the tumor size and position.^(15,16)

In another aspect of the invention, the PEFS can assess verticalstiffness variations of soft materials/tissues up to several centimetersin depth with increased resolution by use of an array of PEFS's ofvarying probe widths ranging from less than 1 mm to several cm.Detection of tissue stiffness both under shear and under compressionwill allow comparison of the stiffness of a hard inclusion such as atumor, with the stiffness of surrounding normal tissue, not only undercompression, but also under shear. Such comparisons will permit adetermination of the interfacial properties between the hard inclusionand surrounding tissue, which has the potential to greatly enhance theability to assess tumor malignancy.

The PEFS is capable of detecting soft-material/stiffness variations inboth the shear and the compression modes while under DC power. Thisallows a portable hand held device to detect soft material/tissuestiffness. Additional advantages result from the ultra-small strainsemployed for detection (smaller than 1%), and the minimal discomfortthat such strains will cause to the patient.

In another aspect of the invention, the PEFS may be fabricated in avariety of shapes including L-shaped, U-L-shaped, U-shaped,square-shaped, O-shaped, tapered, etc. as well as in various lengths andwidths. When the PEFS has an L-shaped tip, the PEFS is capable ofaccurately measuring the shear modulus of soft tissues and materials atvery small strain (<0.1%), a capability most of the current commercialrheological instruments lack.

In addition to detection and mapping of a tumor, the PEFS may also beemployed as a tissue/soft-material mechanical tester, for breast cancerdetection, for prostate cancer detection, for monitoring skin cancer andskin elasticity testing, or for cellular elasticity/plasticitymeasurements using a miniaturized PEFS. Of course, the PEFS is capableof use in conventional methods for making compression and shearmeasurements on pliable materials of any kind and its use need not belimited to tissue measurements.

All-electrical measurement. When a voltage is applied to the top PZTlayer of a PEFS as shown in FIG. 1( b), it causes the PEFS to bend dueto the converse piezoelectric effect, which generates a force, andtherefore, a displacement at the cantilever tip. The bending of thecantilever generates an induced piezoelectric voltage in the bottomsensing PZT layer, which is in proportion to the displacement at thecantilever tip. By carefully monitoring the displacement at thecantilever tip during a given test, an accurate determination of boththe force and displacement exerted on the sample surface can beascertained, which in turn yields an accurate determination of theelastic modulus of the sample. Moreover, by placing a sensing PZT layerin the device, as shown, the maximum of the induced voltage transient ofthe sensing PZT can be used to accurately determine the cantilever tipdisplacement.

The ability of the PEFS to electrically apply a force and electronicallymeasure the displacement makes it ideal for “electronic palpation” likean “electronic finger.” The PEFS measures the tissue compressive (shear)stiffness by touching (rubbing) the tissue surface. The force generationand displacement sensing are all within the “finger.” The PEFS may beused for in-vivo tissue imaging particularly for breast cancer andprostate cancer detection.

The PEPS can measure elastic stiffness and shear modulus of softmaterials, with or without a sensing electrode. In case a sensingelectrode is not used, other means such a laser or piezoelectricdisplacement meter can be provided for displacement determination.

EXAMPLE 1

FIG. 2( a) shows the displacement signal captured by the sensing PZTlayer and by the laser displacement meter when a 10V step potential wasapplied to the unimorph cantilever. FIG. 2( a) shows a typicalall-electrical measurement as displayed on an oscilloscope. The appliedvoltage (line 1), at t=0, indicates the applied voltage was turned on.Line 2 was the voltage output from the laser displacement meter fordirect displacement measurements and line 3 was the induced voltagemeasured at the sensing PZT layer. In FIG. 2( a) the induced voltage wasnegative. The peak of the induced voltage was therefore at minimum neart=0. The induced voltage decayed with time due to the fact that the PZTlayer was not perfectly insulating. The charge generated at the PZTsurface by the cantilever bending dissipated over time. As can be seenfrom FIG. 2( a), the induced-voltage measurement was more sensitive thanthat generated by the commercial displacement meter (Keynce™ LC2450displacemeter (Line 1)) used.

FIG. 2( b) shows the deflection signal captured by the sensing PZT layerat various applied voltages. FIG. 2( b) shows that the induced voltageincreased with the applied voltage.

In FIG. 3, the peak induced piezoelectric voltage captured at thesensing electrode (open squares) and the displacement measured by alaser displacement meter (full circles), versus applied voltage, isshown. As can be seen, the peak induced voltage and the displacement areproportional to each other, validating that the displacement at the tipof the cantilever can be quantified using the peak induced voltagemeasured at the bottom sensing PZT layer.

EXAMPLE 2 Flat-Punch Indentation Compression Test

A flat-punch indentation compression test is a test whereby thecantilever tip is pressed on the sample surface and the cantilevercontact area is much smaller than the sample surface area. This testsimulates an in vivo measurement.

FIG. 4( a) is a representation of an indentation compression test on amodel soft tissue using a PEFS with a sensing PZT layer, and FIG. 4( b)is a schematic of the compression indentation test. In the flat-punchindentation compression tests, the contact area, A, which was muchsmaller than the sample surface, was defined by gluing a thin plasticsheet of a known area on the underside of the cantilever asschematically shown in the setup depicted in FIG. 4( b). Using atraditional Hertzian indentation analysis one can relate load,displacement, contact area, and the mechanical properties of the testedmaterial.¹⁷ When applying a voltage to the top, driving PZT layer, itgenerated a force, F, and caused indentation displacement, δ to thesample. The relationship between the force, F, and the displacement, δ,is described by the following expression.

$\begin{matrix}{{F = {2\sqrt{\frac{A}{\pi}}\frac{E}{l - v^{2}}\delta}},} & (1)\end{matrix}$

wherein ν is the Poisson ratio and E is the Young's modulus of the modeltissue. Denoting the spring constant of the cantilever as K and the“free” displacement generated by an applied voltage V is represented asd₀, the force F exerted on the model tissue by the applied voltage Vwith a displacement, δ, is therefore, F=K(d₀−δ). It follows that theYoung's modulus, E, is then expressed as,

$\begin{matrix}{{E_{i} = {\frac{\sqrt{\pi}}{2}( {1 - v^{2}} )\frac{K( {d_{0} - \delta} )}{\delta \sqrt{A}}}},} & (2)\end{matrix}$

wherein the subscript i of E denotes indentation.

EXAMPLE 3 Regular Compression Test

A regular compression test describes a condition where a cantilever ispressed on the sample surface and the contact area is the same as thesample surface area. A schematic of a regular compression test is shownin FIG. 5( a) where the contact area is the same as the surface area.FIG. 5( b) is a schematic of the deformation of a sample in a regularcompression test under an applied voltage, V. In a regular compressiontest, the elastic modulus is obtained by using

$\begin{matrix}{{E_{c} = \frac{{K( {d_{0} - \delta} )}h}{A\; \delta}},} & (3)\end{matrix}$

wherein h is the height of the sample, d₀ the “free” displacement of thecantilever at voltage V, δ the displacement with the sample, K thespring constant of the cantilever and E_(c) is the elastic modulusmeasured by the regular compression test. For comparison, the same modeltissue sample was tested using both the indentation compression andregular compression test conditions (the left-hand set of data and setupin FIG. 6( a) for regular compression and the right-hand data and setupfor indentation compression in FIG. 6( b)). The elastic moduli, E_(i)and E_(c) were obtained using Eq. (2) and Eq. (3), respectively.Clearly, E_(c) obtained using Eq. (3) under the compression conditionand E_(i) obtained using Eq. (2) under the indentation condition agreedwith each other and also with the known value, 100 KPa, of the elasticmodulus of the rubber employed for the test, thereby validating theelastic modulus measurements using both the indentation test and thecompression test. These results clearly established that the elasticstiffness of tissue can be determined using flat-punch indentation testswith the piezoelectric cantilever of the present invention.

EXAMPLE 4 Tissue-Stiffness Imaging by Indentation Compression

Having demonstrated that piezoelectric cantilevers are capable ofdetermining the elastic stiffness of soft materials using the flat-punchindentation test, and that the test can be done with a driving electrodefor force generation, and a sensing electrode for displacement/forcedetection using all-electrical measurements, here it is demonstratedthat tissue elastic stiffness profiling can be done using flat-punchindentation. A simulated tissue sample with a hard inclusion was madefrom gelatin and candle wax. A 7 mm diameter, 5 mm tall cylinder of waxwas embedded in an 8 mm thick gelatin matrix. Indentation tests wereconducted at 2 mm increments over the entire surface surrounding theinclusion. The elastic modulus at each location was calculated using Eq.(2). The 2-D plot in FIG. 7( a) reflects the higher modulus values inthe center, plainly evident in the corresponding contour plot (FIG. 7(b)). The image was enhanced in FIG. 7( c) through a data smoothingoperation, and is seen in comparison with FIG. 7( d) to depict theapproximate size and shape of the wax.

EXAMPLE 5 Dependence of Depth Limit in Detection on Probe Size

Because the indentation test only needs to press a small part of thesample surface, it is a natural configuration for in vivo application.However, because the probe size is smaller than the sample size in anindentation test, only the volume immediately beneath the indentingdevice is affected by the indentation test. It is thus conceivable thatthe detection sensitivity depends on the depth of the hard inclusion. Todemonstrate this point, the effect of the probe size on the depth limitfor detection using cantilevers of 3 mm width and 5 mm width wasexamined. Both cantilevers are 2 cm in length. The 3 mm wide cantileverhad a contact area of 3 mm (the width)×2 mm and the 5 mm wide cantileverhad a contact area of 5 mm (the width)×2 mm. With the 3 mm widecantilever six wax inclusions of 7 mm diameters at varying depthsbeneath the top surface were embedded in a gelatin sample of 7 mm inheight. For the 5 mm wide cantilever, five wax inclusions 15 mm indiameter were embedded in a gelatin sample of 18 mm in height.Cantilever indentation tests were conducted across the central axis ofeach sample at 1 mm increments. Elastic modulus was calculated at eachlocation using the indentation formula, Equation (2). The result ofelastic profiles of wax inclusions 7 mm in diameter embedded atdifferent depths measured using the 3 mm wide cantilever are plotted inFIG. 8( a). Clearly, the 3 mm wide cantilever could detect the variationin the elastic modulus for depths less than 2-3 mm. When the waxinclusion was at a depth larger than 3 mm, there was no difference inthe elastic modulus measured by the cantilever.

For comparison, the result of elastic profiles of wax inclusions 15 mmin diameter embedded at different depths were measured using the 5 mmwide cantilever and plotted in FIG. 8( b). With a 5 mm wide cantilever,the elastic modulus variation due to the wax inclusion could be detectedat a larger depth. From FIG. 8( b), it can be seen that depth limit onthe detection by a 5 mm long cantilever was about 8 mm. Comparing theelastic modulus profile results measured from the 3 mm and 5 mmcantilevers, it is clear that a wider cantilever (or wider probe)allowed detection of elastic modulus variation at a greater depth. Theeffect of the cantilever width on the detection depth limit is shown inFIG. 8( c).

The above results indicate that one can probe the elastic stiffness todifferent depths by using cantilevers having different probe sizes.Furthermore, by carefully analyzing measurements with different probesizes, it is possible to obtain not only the stiffness variation in thelateral direction, but also in the thickness direction to thereby allowconstruction of 3-D tissue stiffness maps.

EXAMPLE 6 Regular Shear Test

Shear tests can be accomplished using L-shaped cantilevers. A schematicof a regular shear test is shown in FIG. 9. When a voltage was appliedacross the PZT, which is shown as the shaded layer in FIG. 9, it causedthe cantilever to bend, which created lateral movement of the L-shapedtip and sheared the tissue sample underneath. The shear modulus can bedetermined using the equation:

$\begin{matrix}{{G_{c} = \frac{{K( {{\Delta \; x_{0}} - {\Delta \; x}} )}h}{A\; \Delta \; x}},} & (4)\end{matrix}$

where h and A are the height and the surface area of the sample,respectively, K is the spring constant of the cantilever, and Δx₀ and Δxthe displacement of the cantilever without and with the sample,respectively.

EXAMPLE 7 Indentation Shear Test

A schematic of an indentation shear test is shown in FIG. 10. This isthe most relevant condition for potential tissue shear stiffnessmeasurement. When a voltage was applied across the PZT, it caused thecantilever to bend, which created lateral movement of the L-shaped tipand sheared the tissue sample underneath. The shear modulus can bedetermined using the equation:

$\begin{matrix}{{G_{i} = {\frac{\sqrt{\pi}}{2}( {1 - v^{2}} )\frac{K( {{\Delta \; x_{0}} - {\Delta \; x}} )}{\Delta \; x\sqrt{A}}}},} & (5)\end{matrix}$

wherein A is the contact area, ν is the Poisson ratio, K is the springconstant of the cantilever, and Δx₀ and Δx are the displacements of thecantilever without and with the sample, respectively.

EXAMPLE 8 Comparison of All Four Measurements

For comparison of all four measurements, regular compression,indentation compression, regular shear and indentation shear, acantilever that has a U-shaped stainless steel tip as shown in FIGS. 11(a)-11(d) was used. The advantages of such U-shaped tips include: (1)precise control of the contact area in all measurement geometry, and (2)the ability to allow the cantilever to be protected during measurementsin tight spaces as illustrated by (e). The cantilever had a driving PZTlayer 23 mm long, and a sensing PZT layer 10 mm long. The cantilever is4 mm wide.

Both the driving and sensing PZT layers are 127 μm thick and thestainless steel layer is 50 μm thick. The measurements were done onrubber samples with a Young's modulus of 400-500 kPa.

The results of the regular compression, indentation compression, regularshear, and indentation shear measurements on rubber samples that had aYoung's modulus of 400-500 kPa using the U-shaped cantilever as shown inFIGS. 11( a)-11(e), are summarized in FIG. 12. The Young's modulusobtained from regular compression with Eq. (3) and the shear modulusobtained from regular shear measurements with Eq. (4) were 460 kPa and148 kPa, respectively, giving a Poisson ratio of 0.5, consistent withwhat was expected of rubber samples. Using a Poisson ratio of 0.5, theYoung's modulus and shear modulus obtained from indentation measurementswith Eqs. (2) and (5) were 452 kPa and 141 kPa, respectively, in closeagreement with the values obtained from the regular compression andregular shear measurements. The results shown in FIG. 12 validate themeasurement of the Young's modulus using either the regular compressiontest or the indentation compression test, and validate the measurementsof the shear modulus using either the regular shear test or indentationshear test.

EXAMPLE 9 Distinguishing Tumor Interfacial Properties by IndentationShear Tests

Two tumor models, one with a smooth face and the other with a rough facewere made of play dough and were the same size and embedded at the samedepth in the model tissue gelatin as shown in FIG. 13. Both thesmooth-surfaced tumor and the rough-surfaced tumor were 2 mm beneath thegelatin surface. Indentation compression and indentation shear testswere carried out on the plain gelatin surface (point A), and on thegelatin surface above the center of the smooth-surfaced tumor (point B),and above the center of the rough-surfaced tumor (point C). FIG. 14shows the Young's modulus and shear modulus measured on plain gelatin(point A), the smooth-surfaced model tumor (B), and the rough-surfacedtumor (C) using the indentation compression and the indentation sheartests.

While both the smooth-surfaced and rough-surfaced model tumors were muchstiffer than the surrounding gelatin under compression, only therough-surfaced tumor displayed a stiffer shear. This indicates that therough-surfaced tumor model was less mobile than the smooth-surfacedtumor model under shear. Thus, the indentation shear measurement with apiezoelectric finger was effective in probing tumor interfacialproperties and tumor mobility. Combining both the compression and sheartests offers the potential of not only measuring the stiffness, but alsodetermining the mobility of a tumor, which has great potential for tumormalignancy detection.

EXAMPLE 10 Detecting Small Satellite Tumor Missed in PreoperativeScreening

The use of the PEFS in excised breast tumors has been evaluated in thelaboratory. The lumpectomy specimen was from a 60-year old woman withbreast cancer. The known malignancy was 1.4 cm in the largest dimension.After surgical excision, the specimen was oriented with silk sutures,scanned with ultrasound, and images were stored. The PEFS scan wasperformed in the same orientation to allow later correlation with theultrasound image. The specimen was sectioned in the same orientation toallow histological confirmation of the PEFS findings as well. Using thePEFS, preliminary elastic modulus measurements were performed on breastlumpectomy samples using an 8 mm wide PEFS with a rectangular tip. FIG.15 shows lateral elastic modulus profile of a lumpectomy sample measuredby an 8 mm wide PEFS at (a) along y=0 which exhibited two tumors, alarger one at x=17-25 mm, and a smaller one at x=5-10, and at (b) alongy=4 mm, which only exhibited the larger tumor at x=17-25. The dottedrectangles are meant to guide the eye. The PEFS could distinguish thecancers from the surrounding tissues.

Of note, the PEFS scan identified the known 15×13×12 mm invasive ductalcarcinoma at x=15-25 mm and identified a smaller 6×5×3 mm satelliteinvasive ductal carcinoma at x=5-10 mm. This smaller lesion was notdetected by mammogram, ultrasound or the physician's preoperativepalpation.

EXAMPLE 11 Comparison of Shear Modulus to Elastic Modulus Profile ofBreast Cancer

With the second lumpectomy sample (not shown), the elastic modulus, E,and shear modulus, G, profiles have been performed. The tumor was 12-10mm in size and 5 mm below the surface. The tissue was examined with an 8mm wide PEFS. FIG. 16 shows (a) Young's modulus (E) and shear modulus(G) profiles, and (b) G/E profile on breast tissue with cancer. Theresultant elastic modulus and shear modulus profiles are shown in FIG.16( a). Clearly both the elastic modulus and the shear modulus were muchhigher in the region with the tumor than in the surrounding tissue. TheG/E profile is plotted in FIG. 16( b). The G/E ratio was much higher(approaching 0.6-0.7) in the tumor region than that of the surroundingtissues (around 0.3-0.4). The G/E ratio of 0.3 in the normal tissueregion was expected of an isotropic material with a Poisson's ratio of0.5.² A much higher G/E ratio in the cancer region indicated that thetumor was harder to move under shear than under compression as comparedto the surrounding normal tissue. The pathological session resultconfirmed the malignancy.

EXAMPLE 12 Simultaneous determination of Depth and Elastic Modulus ofTumors Using Two PEFS's of Different Widths

In FIG. 17 parts (a) and (b), are shown the lateral elastic modulusprofiles of a 15 mm diameter model clay tumor in gelatin with 2.4 mm(part (a)), and 5.4 mm (part (b)) depths, as respectively measured by a4 mm wide (the open squares) and an 8 mm wide PEFS (the open squares).The lateral location of the clay was marked by the gray shadedrectangle. Comparing the profiles obtained with 8 mm wide PEFS and thoseobtained by the 4 mm wide PEFS, one can see that far away from theinclusion, the values of the elastic modulus of the gelatin obtained byboth PEFS's were essentially the same, indicating no inclusionunderneath. Proximate to the inclusion, the values of the measuredelastic moduli differed between the two PEFS' as they had differentprobe depths.

A separate experiment (not shown) has determined that the probe depth ofa PEFS is twice the PEFS's width. With E_(gel) obtained from locationsfar away from the inclusion, one can then use the two profiles measuredwith the two PEFS' to solve the following two equations for the twounknowns, E_(inclusion) and d:

$\begin{matrix}{{\frac{d_{p,1}}{E_{{measured},1}} = {\frac{d}{E_{gel}} + \frac{d_{p,1} - d}{E_{inclusion}}}},} & (6) \\{{\frac{d_{p,2}}{E_{{measured},1}} = {\frac{d}{E_{gel}} + \frac{d_{p,2} - d}{E_{inclusion}}}},} & (7)\end{matrix}$

where d_(p,1) and d_(p,2) (E_(measured,1) and E_(measured,2)) are theprobe depths of PEFS 1 and PEFS 2, respectively, E_(gel) the elasticmodulus of gelatin that can be obtained from far away from theinclusion, and d and E_(inclusion) are the inclusion depth and theelastic modulus of the inclusion. Using the measured elastic modulusover the top of the center of the inclusion, the known probe depths, andthe E_(gel) obtained from far away from the inclusion and solving Eqs.(6) and (7), we obtained d=2.4 mm and E_(inclusion)=109 kPa from FIG. 17part (a) and d=5.4 mm and E_(inclusion)=102 kPa from FIG. 17 part (b).Both the deduced inclusion depths and E_(inclusion) are in agreementwith the independently measured values: 2.4 mm, 5.4 mm, and 104 kPa,respectively. This clearly illustrates that lateral elastic modulusprofiles measured with two PEFS' of different widths can be used todirectly deduce both the inclusion depth and the inclusion elasticmodulus. With more PEFS', it should be possible to obtain even moredetailed axial elastic modulus profile information.

EXAMPLE 13 Direct Tumor Mobility Measurement Using Two PEFS'

In this model study, a model smooth tumor (the shaded inclusion in theback of FIG. 18) and a model rough (malignant) tumor (the white roughball in the front of FIG. 18) were prepared. Direct tumor mobilitymeasurement was carried out with one PEFS pushing on the side of thetumor and the other PEFS determining the movement of the tumor on theother side. With the driving PEFS pushing down 50 μm, a movement of 2 mmfrom the smooth inclusion and no movement from the rough inclusion weremeasured. This illustrated the sensitivity of the PEFS to directlymeasure tumor mobility for potential malignancy screening.

Preliminary measurement on breast tissues after surgery have indicatedthat a PEFS can detect cancerous tumors as small as 3 mm in size thatwere missed by mammography, ultrasound, and physician's palpation,offering great potential for early breast cancer detection. Furthermore,it was demonstrated that by using two or more PEFS's of differentwidths, one can simultaneously determine both the tumor elastic (shear)modulus and its depth. In addition, it has also been demonstrated thattumor mobility can be assessed by measuring the ratio of the shearmodulus to the elastic modulus of a tumor, or by sensitive direct tumormobility measurement using two PEFS's, one for pushing and one formeasuring the movement. The tumor mobility measurement offers thepotential for non-invasive breast cancer malignancy screening.

It is to be understood, however, that even though numerouscharacteristics and advantages of the present invention have been setforth in the foregoing description, together with details of thestructure and function of the invention, the disclosure is illustrativeonly, and changes may be made in detail, especially in matters of shape,size and arrangement of parts within the principles of the invention tothe full extent indicated by the broad general meaning of the terms inwhich the appended claims are expressed.

The below list of references is incorporated herein in their entirety.

¹ Wellman, R. D. Howe, E. Dalton, K. A. Kern, “Breast Tissue Stiffnessin Compression is Correlated to Histological Diagnosis,”http://biorobotics.harvard.edu/pubs/mechprops.pdf.

² http://www.zfm.ethz.ch/e/res/bio/#Overview.

³ http://www.tainst.com/products/rheology.html

4 R. Ferrini, E. Mannino, E. Ramsdell, and L. Hill, “ScreeningMammography for Breast Cancer: American College of Preventive MedicinePractice Policy Statement,”http://www.acpm.org/breast.htm.

5 A Keller, R Gunderson, O Reikeras, J I Brox, “Reliability of ComputedTomography Measurements of Paraspinal Muscle Cross-sectional Area andDensity in Patients with Chronic Low Back Pain,” SPINE 28 (13):1455-1460, Jul. 1 (2003).

6 V. Straub, K. M. Donahue, V. Allamand, R. L. Davisson, Y. R. Kim, andK. P. Campbell, “Contrast Agent-Enhanced Magnetic Resonance Imaging ofSkeletal Muscle Damage in Animal Models of Muscular Dystrophy,” Magneticresonance in medicine 44:655-659 (2000).

7 L. Gao, K. J. Parker, R. M. Leaner and S. F. Levinson, “Imaging of theelastic properties of tissue-A review,” Ultrasound in Med. & Biol.,22[8], 959-77 (1996).

8 O. Kwon, “T-scan Electrical Impedance Imaging system for anomalydetection.” http://parter.kaist.ac.kr/imi/data/Tscan.doc.

9 S. G. Garlier, C. L. de Kotre, E. Brusseau, J. A. Schaar. P. W.Serruys, and A. F. W. van der Steen, “Elastography,” Journal ofCardiovascular Risk, 9: 237-245 (2002).

¹⁰ E. D. Rosenberg, W. C. Hunt, and M. R. Williamson, Radiology 209, 511(1998).

¹¹ S. A Kruse, J. A. Smith, A. J. Lawrence, M. A. Dresner, A. Manduca,J. F. Greenleaf, and R. L. Ehman, “Tissue Characterization usingMagnetic Resonance Elastography: Preliminary Results,” Phys. Med. Biol,.45 1579-1590 (2000)

¹² L. S. Wilson, D. E. Robinson, and M. J. Dadd, “Elastography—theMovement Begins,” Phys. Med. Biol., 45 1409-1421 (2000)

¹³ Wellman, P. S, Dalton, E. P., Krag, D., Kern, K. A., Howe, R. D.“Tactile Imaging of Breast Masses: First Clinical Report,” Archives ofSurgery 136 (2), 204-08 (2001)

14 J. F. Greenleaf, M. Fatemi, M. Insana, “Selected Methods for ImagingElastic Properties of Biological Tissues,” Annu. Rev. Biomed. Eng. 5,57-78 (2003)

¹⁵ P. S. Wellman, R. D. Howe, N. Dewagan, M. A. Cundari, E. Dalton, andK. A. Kern, “Tactile Imaging: A Method For Documenting Breast Lumps,”http://biorobotics.harvard.edu/pubs/tactile.pdf.

¹⁶ Y. Wang, C. Nguyen, R. Srikanchana, Z. Geng, M. T. Freedman, “TactileMapping of Palpable Abnormalities for Breast Cancer Diagnosis,”http://www.imac.georgetown.edu/members/resumes/..%5CWebServer%20Documents%5CDoc_P_(—)22_F.pdf.

1. A sensor system comprising: a cantilever including: a piezoelectriclayer, wherein a portion of said piezoelectric layer forms an exposedcontact surface for contacting a sample; an apparatus for generating aforce in said cantilever; and a means for measuring a displacement ofsaid piezoelectric layer resultant from said generated force.
 2. Thesensor system of claim 1, wherein the means for measuring a displacementof said piezoelectric layer comprises an apparatus for measuring avoltage, wherein the measured voltage is indicative of the displacement.3. The sensor system of claim 1, wherein the means for measuring adisplacement of said piezoelectric layer is selected from the groupconsisting of: a laser and a piezoelectric displacement meter.
 4. Thesensor system of claim 1, wherein the cantilever further comprises asecond piezoelectriclayer and the piezoelectric layers are electricallyseparated from one another, and wherein said sensor is capable ofsimultaneously inducing a force in said cantilever and measuring adisplacement of one said piezoelectric layer.
 5. The sensor system ofclaim 4, wherein said second piezoelectric layer comprises a portionthat extends beyond the other piezoelectric layer and wherein saidportion has a shape selected from the group consisting of: asubstantially square-shaped configuration, a substantially Lshapedconfiguration, a substantially U-shaped configuration, a substantiallyO-shaped configuration and a tapered configuration.
 6. The sensor systemof claim 4, wherein said second piezoelectric layer comprises a portionthat extends beyond said first piezoelectric layer and wherein saidportion is oriented at an angle greater than or less than 180 degreeswith respect to said first piezoelectric layer.
 7. The sensor system ofclaim 6, wherein said portion is oriented at about a 90 degree anglewith respect to a remainder of said second piezoelectric layer.
 8. Thesensor system of claim 1, comprising two or more of said cantilevers,and wherein at least two of said cantilevers have different dimensions.9. The sensor system of claim 8, wherein the at least two cantilevershave different widths.
 10. A sensor system comprising: a cantileverincluding: a first piezoelectric layer enabled to provide a force; asecond piezoelectric layer; an apparatus for applying a voltage to saidfirst piezoelectric layer to generate a force in said cantilever; ameans for measuring a displacement of said second piezoelectric layerresultant from said generated force.
 11. A sensor system as claimed inclaim 10, wherein said piezoelectric layers are the same length.
 12. Asensor as claimed in claim 10, wherein a portion of a surface of atleast one said piezoelectric layer forms an exposed surface portion forcontacting a sample.
 13. A sensor as claimed in claim 10, wherein saidfirst and second piezoelectric layers are electrically isolated from oneanother.
 14. A method for determining a compression modulus of asubstrate comprising the steps of; a cantilever sensor including apiezoelectric material, wherein said sensors are in contact with asubstrate comprising a target; applying a compressive force to thesubstrate via a sensor having a cantilever including a piezoelectricmaterial, when said sensor is in contact with the substrate; detecting adisplacement of the cantilever due to said compressive force;determining a compression modulus of said substrate from said detecteddisplacement.
 15. The method of claim 14, further comprising the step ofdetermining a depth of a target located within the substrate.
 16. Themethod of claim 14, wherein the step of determining the compressionmodulus comprises determining the compression modulus at a plurality ofdifferent depths within the substrate.
 17. The method of claim 14,wherein said target is a tumor or tissue surrounding a tumor.
 18. Amethod for determining a shear modulus of a substrate comprising thesteps of; applying a shear force to said substrate via a sensor having acantilever including a piezoelectric material when said sensor is incontact with the substrate; detecting a displacement of the cantileverdue to said shear force; and determining a shear modulus of saidsubstrate from said detected displacement.
 19. The method of claim 18,wherein said substrate is a tumor or tissue surrounding a tumor.
 20. Themethod of claim 19, wherein a plurality of said sensors are employed insaid method in an array and further comprising at least one stepselected from the group consisting of: mapping a tumor, determiningtumor stiffness and determining tumor mobility.